In this project, our objective is to develope the structural study of Dynamic Programming(DP in short) and establish DP method which is more robust or more flexible in the sense that it is reasonably efficient in rough approximation and allows for fluctuating factors in sequential decision processes.For this purpose. we tried to develope analytical studies on various mathematical decion model.(1) Markov set-chain model As a model which is robust for rough approximation of the transition matrix in Markov decision processes, we introduced a decision model, called a controlled Markov set-chain, and derived a DP equation by which Pareto optimal policies was constructed. Some computational results are included.(2) Fuzzy dynamic systems and stopping problem The ergodic theorem for the dynamic system with fuzzy state and fuzzy transition is developed and the existence and uniqueness of solutions of the corresponding DP equations is proved. Also, a stopping problem for dynamic fuzzy system is formulated and solved by an extended UP method.(3) General utility model A stopped Markov decision process is analysed under general utility. The corresponding DP equation is described by a family of distributions and more usefull in application of DP.さらに,ファジィ・ストピンングルール(fuzzy stopping rule)を導入して,ファジィ動的システムの最適停止問題を定式化し,D.P.の適用可能性の検討を通して,D.P.の適用範囲を拡大した.3. 一般効用モデル一般効用関数のもとでのマルコフ決定過程の期待効用最大化問題を,政策をパラメータとする分布族に依ってD.P.方程式を記述し最適解の存在とその特徴付けを行った.得られた結果は,指数型の従来の幾つかの結果を特別の場合に含み,動的計画法の適用範囲を拡大することに成っている.これらの研究結果は,学術論文に掲載又は掲載予定である。